"Grasshopper" or "inchworm"? (maths related)

Naikon

Which "breed" of maths person are you?
The former is used to describe someone who thinks about maths outside school and doesent look at it like something you "just do".
For instance I usually think about problems a good bit and if possible always use other methods to solve the same problem, just to see if its possible.
For example I was solving a few algebraic equations today when suddenly I heard:
"OMFG WTF are ya doin?"

My friend didnt believe in using "other" methods to solving problems much to the same response of the teachers "the Examiner wont accept that!, do it my way" line.
I mean maths should be more about conceptual thinking and less about rigid rote step learning?
what if there is a variation in the exam questions?
If It warrants the same answer then why not be a little "creative"
Has the LC system perverted the true meaning of maths:D?

The latter believes that maths is something you rote learn to a varying degree without really understanding or appreciating the concept behind what you are learning.
just that it will get you points.
Most of my class fit the latter.

Opinions:D

JC 2K3

Grasshopper, although why the terminology?

I do the least amount of study for maths out of all my subjects and tbh it's one of the easiest subjects I do(behind Irish).

You either find it very easy or very hard, that's what I find anyway.

Citizen_Erased

Damnit , managed to vote for the wrong one. I'm the one that uses alternate methods and has to understand everything (although I seem to struggle with your terminology ).But what annoy me are the people who just have to understand even though they can't and never will and can slow up the flow of a class by asking silly irrelevant abstract questions.
Lol , I nearly passed this thread thinking it was some sorta biology related thing.

PurpleFistMixer

I find if you don't understand the concept of what you're doing it makes solving the questions immensely difficult. It turns it from a slightly lateral thinking exercise to trying to learn off the different approaches to questions based on how you look because you have no idea what you're doing. And... well, I really don't like having to learn off stuff, so thank god maths isn't like that for me.

Only 8 people in my class, so we never get irrelevant questions! I tend to ignore the teacher most of the time, anyway... my class just tend to sit there doing questions and if anyone has a problem or if we're doing something new and difficult, then he'll explain it. Tis a fine way of doing it.

Naikon

But If you understand how the teacher teaches a question using the standard method, it can more efficient using quicker methods.
I showed one of my mates recently How to do synthetic Division with cubic equations as he understood the main method but usually made a small mistake thus losing marks.
These things make a difference in Maths exams.
different methods are handy in probability too.
You have to understand most concepts Irrespective of your method(not in all cases granted)

ZorbaTehZ

OFC I think about maths out side school, what do you take me for, a normal person?

Naikon wrote:

For example I was solving a few algebraic equations today when suddenly I heard:
"OMFG WTF are ya doin?"

My friend didnt believe in using "other" methods to solving problems much to the same response of the teachers "the Examiner wont accept that!, do it my way" line.

Please expand on that.:)

Raphael

/me is currently studying TP after his A1 in higher maths...

fuinneamh

Ths poll is beginning to say a lot about the people who frequent this site...

JC 2K3

fuinneamh wrote:

Ths poll is beginning to say a lot about the people who frequent this site...

In what way?

md99

Inchworm all the way, not a big fan of maths but I like how a lot of it can be done with formulae, effort and a little natural ability. I don't know what anything is there for, standard deviation etc, and don't want to know either, unless the LC needs me to know, then I'll want to know all about it... LC Maths will be the last maths I'll ever do...

wish the same could be said for Irish, there's two Irish exams when qualifying in law... even if they are very easy ones.

dan719

As in we are all maths and physics nerds. 'One day the nerds shall inherit the earth'.I like to take this as we shall understand it, and no one else will!:D :rolleyes: Go Grasshoppers. Although I would prefer a beaver(a true nerd will understand)

lemansky

dan719 wrote:

Although I would prefer a beaver(a true nerd will understand)

Yes i do:D Grasshopper all the way!Maths is just a wasted exercise if you don't understand the stuff.The people in my year who see it as an exercise in rote learning are the ones who don't ever see beyond the book and acknowledge the applications of what we learn, they just see it as a dead and boring subject which is fair enough, everyone to their own, but they then start calling it useless in the real world and this all stems from their attitude to learning it,even those who learn it by repitition and are actually pulling good grades:mad: :mad:

dan719

Go beavers go. Yes the rote learning type.:mad: :mad: :mad: They merely distract from the beauty and elegance of maths! And really annoy me too.
Consider the following true story.

the binomial expansion of
(1+x)^n=1+n!dividedby2!.x......
therefore
(2)^n=....

inchworm; Sir where did you get the two from?
Teacher; I let x=1 inchworm
Cue laughter.
He got a b in his mocks.

Selphie

md99 wrote:

I don't know what anything is there for, standard deviation etc, and don't want to know either, unless the LC needs me to know, then I'll want to know all about it... LC Maths will be the last maths I'll ever do...

Couldn't agree more

Naikon

dan719 wrote:

the binomial expansion of
(1+x)^n=1+n!dividedby2!.x......
therefore
(2)^n=....

inchworm; Sir where did you get the two from?
Teacher; I let x=1 inchworm
Cue laughter.
He got a b in his mocks.

:rolleyes:

Absolut

Rote learning seems to pay off a lot more than actually understanding the material, especially when you get to college. I'm not saying rote learning is a good thing, but it's definetly better rewarded.

JC 2K3

No it's not....

Rote learning = spending HOURS study on maths to get the required grade.
Understanding = much less studying involved and you still get a good grade.

If you understand it you don't need to rote learn as it simply makes sense.

ZorbaTehZ

Absolut wrote:

Rote learning seems to pay off a lot more than actually understanding the material, especially when you get to college. I'm not saying rote learning is a good thing, but it's definetly better rewarded.

I hope you're joking.

dan719

Absolut wrote:

Rote learning seems to pay off a lot more than actually understanding the material, especially when you get to college. I'm not saying rote learning is a good thing, but it's definetly better rewarded.

I disagree. If you cannout understand something, no matter how much you study it, you will never be able to fully explain it, or explore its implication. eg in physics. you can learn a definition for the photoelectric effect and the experiments related to it. But when asked what affects the number of electrons released (for example) you won't know. Unless you understand how it works. Subjects such as maths and physics are not amenable to rote learning because they are so vast. You cannot learn off everything. There must be some understanding.

Thomas_S_Hunterson

I think it's such a shame with maths that people are always giving out about it that it's too hard and so on. It's maths. It's not supposed to be a subject that you can just learn like business or history, you either have a natural aility or you don't.

If you don't it takes a hell of a lot of work to get a good grade, but it still doesn't give you the right to complain aout the likes of the pyramid photo question from last year, just because your teacher didn't give you an exact step by step run through of the question beforehand.

The question was easy. People who were good at maths could do it and got their As, the people whodo not have a natural ability complained about it when they couldn't do it. Questions like that are there to catch out the rote learners who do not have a natural ability.

Absolut wrote:

rote learning seems to pay off a lot more than actually understanding the material, especially when you get to college. I'm not saying rote learning is a good thing, but it's definetly better rewarded.

So doing more work for the same reward means you are better rewarded? personally I feelthe lower work:reward ratio the better

Absolut

sean_keevey wrote:

So doing more work for the same reward means you are better rewarded? personally I feelthe lower work:reward ratio the better

No, my point is that to understand a lot of the stuff you need for college exams means that you'd have to spend hours and hours trying to research it. Whereas if you have a solution that you can just memorise and regurgitate in an exam, you'll get all the marks for a fraction of the work.

My original post said that it applies more to college - less so for the leaving cert. When you're studying maths in college, it's mostly theory that's asked in exams are generally just pages and pages of proofs. And exams are generally very similar from year to year. It's a lot easier just to learn a page then to spend hours trying to understand it. And from what I've seen, the people who have no clue what's goin on in a course, but have good short term memory and cram for exams two weeks beforehand, do equally well if not better than the people who spend hours studying the subject consistently.

So the "lower work : reward ratio" that you mention is more applicable to rote "learning" than actually learning.

I disagree. If you cannout understand something, no matter how much you study it, you will never be able to fully explain it, or explore its implication.

As I said above, for most undergrad exams, it's perfectly feasible to get a 1.1 without ever understanding the subject. You wont understand what you're writing, or be able to use it again (or even remember it a month later), but for most maths courses you'll still come out of the exam with as good a grade as the person who understands it all.

dan719

You don't have to study something for hours to understand it. and to learn a proof of it, you have to understand at least someof it, otherwise it just becomes a case of learning a dense page of symbols and letters, which mean absolutely nothing.

Absolut

dan719 wrote:

You don't have to study something for hours to understand it. and to learn a proof of it, you have to understand at least someof it, otherwise it just becomes a case of learning a dense page of symbols and letters, which mean absolutely nothing.

Very often it does take an hour or two to understand a proof. And when it takes you two hours to understand it (without learning it so that you can get it word perfect in an exam), and there are 15-25 other large proofs on the course, it can get very tedious trying to understand them all and then go back to learn them all properly.

As I said before, it doesn't apply so much to the leaving cert (since there aren't very many (any?) long proofs).

dan719

But my argument would be that you can produce something by understanding the steps involved. I.e by understanding it you are learning it. Where are you studying maths btw?(I get the impression you are obviously)

Undergod

Grasshopper, kinda.

I can sometimes struggle with maths till I understand _why_ that does that, why that formula works. I particularly had this problem in co-ordinate gemoetry a few years back, until I could visualise what I was actually doing.

But maths is often fun and enjoyable I find, and I will occasionally follow tangents of my own thoughts away during class.

md99

Absolut wrote:

Very often it does take an hour or two to understand a proof. And when it takes you two hours to understand it (without learning it so that you can get it word perfect in an exam), and there are 15-25 other large proofs on the course, it can get very tedious trying to understand them all and then go back to learn them all properly.

as an inchworm I agree completely (man I hate that title), I never thought I'd ever know or understand any... I was planning on coasting by without them.. well, I learned them with little trouble once I'd the basic a/b knowledge after the pres, now I'd be ecstatic if any of them came up... I'd love another paper like the 1997 one (ie 4 proofs came up)

I think the proofs are mostly simple once you've ALL the basics covered... it's usually just one step in each of them that one has to learn.. even the perp. distance theorem so many inchworms dread. two simple steps, get the area in two different ways and let equal...

dan719

Absolut wrote:

Very often it does take an hour or two to understand a proof. And when it takes you two hours to understand it (without learning it so that you can get it word perfect in an exam), and there are 15-25 other large proofs on the course, it can get very tedious trying to understand them all and then go back to learn them all properly.

As I said before, it doesn't apply so much to the leaving cert (since there aren't very many (any?) long proofs).

The bit that md99 left out.;) It certainly does not take any length of time to understand any of the proofs on the leaving cert course.

JC 2K3

Absolut wrote:

Very often it does take an hour or two to understand a proof. And when it takes you two hours to understand it (without learning it so that you can get it word perfect in an exam), and there are 15-25 other large proofs on the course, it can get very tedious trying to understand them all and then go back to learn them all properly.

As I said before, it doesn't apply so much to the leaving cert (since there aren't very many (any?) long proofs).

Well it prob gets much more difficult with university maths. But personally i never bother learning LC proofs out of the book. With some I'll memorise the picture and/or basic starting point, but after that I just try to prove them myself(sometimes with a pretty different method to the book) and it works out 90% of the time.

dan719

Of course university maths is much harder. We have had that conversation on other threads. You cannot compare a proof that may be four or five pages long, which uses several disparate areas of mathematics, to the proof of the cosine rule:rolleyes:

JC 2K3

dan719, stop being such a pretentious, condescending cúnt at every oppertunity.

I never said university maths wasn't hard.....

cocoa

Absolut wrote:

As I said above, for most undergrad exams, it's perfectly feasible to get a 1.1 without ever understanding the subject. You wont understand what you're writing, or be able to use it again (or even remember it a month later), but for most maths courses you'll still come out of the exam with as good a grade as the person who understands it all.

roflmao, you post your own personal opinion as though it is fact in a forum where there's only leaving cert students, so who the hell is going to disagree, right?
I'd be highly curious to see what a poll about rote learning in uni would yield in one of the uni forums. Personally I wouldn't have any respect for a uni which hands out degrees for that...